Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pi 3.14159265
#define mod 1000000007
#define pb push_back
#define N 100002
#define FAST  ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define FF fflush(stdout);
#define lcm(a,b) (a*b)/__gcd(a,b)
int main()
{
    FAST
    ll a,b,k,i;
    cin >> a >> b >> k;
    string x,y;
   /* if(k>0 && (a==0 || b==1 || k>a+b-2) )
    {
        cout << "No\n";
        return 0;
    }*/
    for(i=0;i<a+b;i++)
    {
        if(i<b)x=x+'1';
        else x=x+'0';
    }
    y=x;
    ll q=b-1;
    while(k && q<a+b-1 && q>0)
    {
        swap(y[q],y[q+1]);
        q++;
        k--;
    }
    q=a+b;
   for(i=0;i<a+b-1;i++)
   {
       if(y[ i ]=='0')
       {
           q=i;
           break;
       }
   }
   while(k && q>1 && q<a+b)
   {
       if(y[q]=='0' && y[q-1]=='1')
       {
           swap(y[q],y[q-1]);
           q--;
           k--;
       }
       else break;
   }
   if(k)cout << "No";
   else
   {
       cout << "Yes" << endl;
       cout << x << endl << y << endl;
   }
}